Problem B and Solution

'Temp'ting Crickets

Crickets can help determine the temperature, in degrees Celsius. One possible way to make this calculation is to follow the steps below.

Step 1: Count the number of chirps in \(25\) seconds.

Step 2: Divide the number from Step 1 by \(3\).

Step 3: Add \(4\) to the number from Step 2.

By filling in each \(\underline{\ \ \ \ \ }\) in the following equation with either a variable or a number, write an equation to show how to get the temperature, \(t\), based on a certain number of chirps, \(c\), in \(25\) seconds. \[t = \underline{\ \ \ \ \ }\div \underline{\ \ \ \ \ }+\underline{\ \ \ \ \ }\]

Fill in the second column of the following table.

Chirps (\(c\)) in \(25\) seconds Temperature (\(t\)) in degrees Celsius \(60\) \(54\) \(66\) Fill in the first column of the following table.

Chirps (\(c\)) in \(25\) seconds Temperature (\(t\)) in degrees Celsius \(18\) \(20\) \(16\)

To determine the temperature, \(t\), we take the number of chirps in \(25\) seconds, \(c\), divide by \(3\), then add \(4\). That is, \(t = \underline{\,c\,}\div\underline{\,3\,}+\underline{\,4\,}\).

You may use the given steps or the equation from part (a) to fill in the table.

For example when there are \(60\) chirps, we divide by \(3\) to get \(20\), and then add \(4\) to get \(24\) degrees Celsius.

Or we may use the equation \(t = 60 \div 3 + 4 = 20 + 4 = 24\).

Chirps (\(c\)) in \(25\) seconds Temperature (\(t\)) in degrees Celsius \(60\) \(24\) \(54\) \(22\) \(66\) \(26\) To find the number of chirps for a given temperature, we work backwards, reversing the steps as we go. That is, we subtract \(4\) from the given temperature, and then multiply by \(3\).

For example when the temperature is \(18\) degrees Celsius, we subtract \(4\) to get \(14\), and then multiply \(14\) by \(3\) to get \(42\) chirps.

The equation to calculate chirps, \(c\), given temperature, \(t\), is \(c=(t-4)\times 3\).

Chirps (\(c\)) in \(25\) seconds Temperature (\(t\)) in degrees Celsius \(42\) \(18\) \(48\) \(20\) \(36\) \(16\)